perplexus.info :: Numbers : Power Crossed Cube Conclusion

Power Crossed Cube Conclusion (Posted on 2023-04-01)

Determine all triplet(s) (p, q, r) of positive integers that satisfy the equation:

          (5)^p * (43)^q + 1 = r³

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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computer solution

| Comment 1 of 3

for px=1:50

p=sym(px);

for qx=1:50

q=sym(qx);

rc=5^p*43^q+1;

r=rc^(1/3);

if r==floor(r)

disp([p q r rc])

end

finds only

[1, 1, 6, 216]

i.e.,

p = 1

q = 1

r = 6

r^3 = 216 = 5*43 + 1

Posted by Charlie on 2023-04-01 11:29:11

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